Particle size distribution measuring apparatus

ABSTRACT

In order to reduce a calculation time of a particle size distribution, a particle size distribution measuring apparatus includes an operation part for receiving light intensity signals outputted from photodetectors and calculating a particle size distribution of the particles based on the fact that a vector s is represented by a predetermined expression including a product of a vector q and a coefficient matrix K, and the operation part is adapted to calculate values of a plurality of first parameters that depend on the particle sizes of the particles and a plurality of second parameters that depend on spread angles of the diffracted/scattered lights, wherein the first and second parameters are used for calculating one element among elements of the coefficient matrix K, and at least one of these calculated values is stored to be used for calculating another element of the coefficient matrix K.

CROSS REFERENCE TO RELATED APPLICATIONS

The present invention claims priority under 35 U.S.C. §119 to JapaneseApplication No. 2013-132141 filed Jun. 24, 2013, the entire content ofwhich is incorporated herein by reference.

TECHNICAL FIELD

The present invention relates to a particle size distribution measuringapparatus for calculating a particle size distribution of particlesbased on a light intensity pattern of diffracted light and/or scatteredlight (also, referred to as “diffracted/scattered light”, hereinafter)caused by irradiation of light to the particles to be measured.

BACKGROUND ART

As disclosed in Patent Literature 1, a particle size distributionmeasuring apparatus of this kind is intended to detectdiffracted/scattered light by a plurality of photodetectors andcalculate a particle size distribution based on the following Expression(1) using a light intensity pattern vector obtained by a value of alight intensity signal outputted from each of the photodetectors.

[Equation 1]

s=Kq  (1)

Here, s is a vector representing a light intensity pattern at everyangle of diffracted/scattered light obtained from a value of a lightintensity signal outputted from each of the photodetectors, q is avector representing a particle size distribution of the particles to bemeasured, and K is a coefficient matrix for converting the particle sizedistribution vector to the light intensity pattern vector.

CITATION LIST Patent Literature

-   Patent Literature 1: JPA 2008-164539

SUMMARY OF INVENTION Technical Problem

By the way, the coefficient matrix K is determined depending on physicalproperties such as a refractive index of the particles, particle sizesand arrangement positions of the photodetectors. Therefore, in order tocalculate the particle size distribution based on the above Expression(1), it is essentially necessary to previously calculate the coefficientmatrix K.

However, in the conventional technic, since each of elements of thecoefficient matrix K is obtained one by one based on such as a Miescattering theory, it takes considerable time for calculation of thecoefficient matrix K.

Therefore, the present invention has been made in consideration ofsolving the problem and its essential object is to reduce a calculationtime of a particle size distribution by reducing the calculation time ofthe coefficient matrix K.

Solution to Problem

That is, a particle size distribution measuring apparatus according tothe present invention includes: a light source for irradiating light toparticles to be measured; a plurality of photodetectors for detectinglight intensities of diffracted/scattered lights caused by theirradiation of the light; and an operation part for receiving lightintensity signals outputted from the respective photodetectors andcalculating a particle size distribution of the particles based on thefact that a vector s is represented by a predetermined expressionincluding a product of a vector q and a coefficient matrix K, and theoperation part is adapted to calculate values of a plurality of firstparameters that depend on the particle sizes of the particles and aplurality of second parameters that depend on spread angles of thediffracted/scattered lights, the first and second parameters being usedfor calculating one element among elements of the coefficient matrix K,and store at least one of the values to be used for calculating anotherelement of the coefficient matrix K.

Here, the vector s is a vector representing a light intensity pattern atevery angle of the diffracted/scattered lights obtained from values ofthe light intensity signals outputted from the respectivephotodetectors, the vector q is a vector representing the particle sizedistribution of the particles to be measured, and the coefficient matrixK is a matrix for converting the vector q to the vector s.

As the predetermined expression, for example, the Expression (1)mentioned above or an expression including a term representing such as,for example, a noise added to this Expression (1) can be exemplified.

With this configuration, since another element is calculated using thevalues of the first parameters and second parameters at the time ofcalculating a certain element, the calculation time of the coefficientmatrix K can be remarkably reduced compared to a conventional case ofcalculating each of the elements one by one by a complicatedcomputation. Thus, it is possible to reduce a time required to calculatethe particle size distribution.

Here, the coefficient matrix K is represented by Expression (2) asfollows:

$\begin{matrix}\left\lbrack {{Equation}\mspace{14mu} 2} \right\rbrack & \; \\{K = \begin{pmatrix}k_{11} & k_{12} & \ldots & k_{1,y} \\k_{21} & \; & \; & \vdots \\\vdots & \; & \; & \vdots \\k_{x\; 1} & \ldots & \ldots & k_{xy}\end{pmatrix}} & (2)\end{matrix}$

Here, x is a number of the photodetectors, and y is a number ofdivisions of the particle size range to be measured.

In this coefficient matrix K, when calculating the elements belonging tothe same row, the second parameters can be used in common, and whencalculating the elements belonging to the same column, the firstparameter can be used in common.

As a specific aspect of the operation part, it is exemplified that theoperation part calculates an element of a position where a certain rowand a certain column intersect using the values of the second parametersstored at a time of calculating the elements included in the row and thevalues of the first parameters stored at a time of calculating theelements included in the column among the elements of the coefficientmatrix K, based on a following Expression (3):

$\begin{matrix}\left\lbrack {{Equation}\mspace{14mu} 3} \right\rbrack & \; \\{{k\left( {m,\alpha,\theta} \right)} = {\sum\limits_{n = 1}^{N}\; {\frac{{2\; n} + 1}{n\left( {n + 1} \right)}\begin{bmatrix}{{{a\left( {n,m,\alpha} \right)} \times {\pi \left( {n,{\cos \; \theta}} \right)}} +} \\{{b\left( {n,m,\alpha} \right)} \times {\tau \left( {n,{\cos \; \theta}} \right)}}\end{bmatrix}}}} & (3)\end{matrix}$

Here, k is a value of each of the elements of the coefficient matrix K,m is a refractive index of each of the particles to be measured, α is avalue associated with each of the particle sizes of the particles to bemeasured, θ is a spread angle of diffracted/scattered light, a and b arethe first parameters that depend on the refractive index of the particleand particle size, π and τ are the second parameters that depend on thediffracted/scattered lights, and N is a value that represents the lastterm when the operating part operates a sum represented by a sigmasymbol.

Advantageous Effects of Invention

According to the present invention configured as described above, itbecomes possible to significantly reduce the calculation time of thecoefficient matrix K as compared to the conventional configuration, andtherefore it is possible to reduce the time required for entiremeasurement.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a schematic diagram showing a particle size distributionmeasuring apparatus in one embodiment of the present invention;

FIG. 2 is a functional block diagram showing a functional configurationof an operation part in the same embodiment;

FIG. 3 is a functional block diagram showing a functional configurationof a coefficient matrix calculation part in the same embodiment;

FIG. 4 is a diagram showing a calculation procedure of the coefficientmatrix calculation part in the same embodiment;

FIG. 5 is a flow chart showing a procedure of calculating an element byan element calculation part in the same embodiment;

FIG. 6 is a diagram for explaining an effect of the particle sizedistribution measuring apparatus in the same embodiment; and

FIG. 7 is a diagram showing a calculation procedure of a coefficientmatrix calculation part in another embodiment.

DESCRIPTION OF EMBODIMENTS

The following describes one embodiment of a particle size distributionmeasuring apparatus 1 according to the present invention with referenceto the accompanying drawings.

The particle size distribution measuring apparatus 1 according to thepresent embodiment is intended to measure a particle size distributionby detecting the diffracted/scattered lights making use of a fact that alight intensity pattern (a light intensity distribution) associated witha spread angle of the diffracted/scattered lights caused uponirradiation of light to the particles is determined by the particlesizes based on Mie scattering theory.

As schematically shown in FIG. 1, the particle size distributionmeasuring apparatus 1 includes an apparatus main body 2 and an operationpart 3.

The apparatus main body 2 includes: a cell 21 for accommodating a sampleof dispersed particles; a laser device serving as a light source 23 forirradiating laser beams to the particle within the cell 21 through alens 22; and a plurality of photodetectors 24(A) and 24(B) for detectinglight intensities of the diffracted/scattered lights caused by theirradiation of the laser beams associated with the spread anglesthereof.

In this configuration, although a batch-type cell is used as the cell 21in the present embodiment, a circulating cell may be also used.

The operation part 3 is physically configured of a general-purpose ordedicated computer including a CPU, a memory, an input/output interface,and the like, and it is intended to receive light intensity signalsoutputted from the respective photodetectors 24(A) to 24(B) andcalculate a particle size distribution based on Expression (1).

This operation part 3 is intended to exhibit at least functions of acoefficient matrix calculation part 31 and a particle size distributioncalculation part 32 by allowing the CPU and peripherals to cooperate inaccordance with a predetermined program stored in a predetermined areaof the memory as shown in FIG. 2. More specifically, referring to thefunctions, the coefficient matrix calculation part 31 is adapted tocalculate the coefficient matrix K and the particle size distributioncalculation part 32 is adapted to calculate a particle size distributionbased on Expression (1) using a light intensity pattern vector s and thecoefficient matrix K obtained from values of the respective lightintensity signals.

In the present embodiment, since the coefficient matrix calculation part31 has specific features, these features are described below.

The coefficient matrix calculation part 31 is intended to calculate thecoefficient matrix K associated with physical properties of theparticles to be measured, particle sizes and arrangement positions ofthe photodetectors 24. In the present embodiment, the coefficient matrixcalculation part 31 is configured to receive values of, for example,refractive indexes of the particles inputted by an operator andcalculate each of elements of the coefficient matrix K associated withthe particle sizes and the arrangement positions of the photodetectors24.

More specifically, as shown in FIG. 3, the coefficient matrixcalculation part 31 has functions serving as: a plurality of elementcalculation parts 4 for calculating the elements based on Expression(3); and a storage part 5 for storing two kinds of first parameters aand b and two kinds of second parameters π and τ that are calculated ina calculation process of each of the element calculation parts 4.

Here, in the present embodiment, the storage part 5 is set in apredetermined area of a cache memory.

As shown in FIG. 3, each of the element calculation parts 4 hasfunctions serving as an operation executing part 41 for executing anoperation based on Expression (3) and a parameter calculation part 42for calculating parameters to be used in an operation executed by theoperation executing part 41.

Thus, in the present embodiment, the coefficient matrix calculation part31 has the same number of the element calculation parts 4 as the number(x) of the rows of the coefficient matrix K, and as shown in FIG. 4,these element calculation parts 4 are configured so as to compute theelements included in one column in parallel and proceed in sequence thisparallel computation from the first column to the last (i.e., y-th)column to thereby calculate all of the elements.

Regarding the parallel computation mentioned here, it is not necessarythat starting or ending of the computations and the like are executed atthe same timing. That is, it may also include a computation state whereeach of the element calculation parts 4 calculates the elements withsome time lags.

Also, these element calculation parts 4 may be configured so as to bemounted on a plurality of personal computers.

Subsequently, a procedure of calculating an element k_(ij) positioned atan intersection of, for example, i-th row and j-th column by the elementcalculation part 4 is described in detail with reference to FIGS. 3 and5 together with an explanation of an operation of each part in theelement calculation part 4. Here, i is an integer in a range of 1≦i≦x,and j is an integer in a range of 1≦j≦y.

In the following description, it is assumed that the refractive index mof the particles is inputted to the coefficient matrix calculation part31 by the operator.

Here, the element k_(ij) indicates a light intensity detected when thediffracted/scattered light caused by the particles of a unit amount ofparticles belonging to a j-th range of divided particle size ranges tobe measured is incident to the i-th photodetector 24 among the pluralityof photodetectors 24. Accordingly, the value a associated with each ofthe particle sizes and the spread angle θ of the diffracted/scatteredlight in Expression (3) represented in obtaining this element k_(ij)become constants, and each of the element calculation parts 4 calculatesthe element k_(ij) based on the following Expression (3)′ including onlyn as a variable.

$\begin{matrix}\left\lbrack {{Equation}\mspace{14mu} 4} \right\rbrack & \; \\{{k_{ij} = {\sum\limits_{n = 1}^{N}\; {\frac{{2\; n} + 1}{n\left( {n + 1} \right)}\left\lbrack {{{a_{j}(n)} \times {\pi_{i}(n)}} + {{b_{j}(n)} \times {\tau_{i}(n)}}} \right\rbrack}}},} & (3)\end{matrix}$

Here, for convenience of the explanation, Expression (4) is put asfollowing:

$\begin{matrix}\left\lbrack {{Equation}\mspace{14mu} 5} \right\rbrack & \; \\{{f(n)} = {\frac{{2\; n} + 1}{n\left( {n + 1} \right)}\left\lbrack {{{a_{j}(n)} \times {\pi_{i}(n)}} + {{b_{j}(n)} \times {\tau_{i}(n)}}} \right\rbrack}} & (4)\end{matrix}$

Further, the following describes the case of n=m as an example.

In the present embodiment, there are included a plurality of firstparameters of one kind in the above Expressions (3)′ and (4) that arerespectively represented as a_(j)(1), a_(j)(2), . . . a_(j)(N).Similarly, there are also included a plurality of first parameters oftwo kinds that are respectively represented as b_(j)(1), b_(j)(2), . . .b_(j)(N).

In the present embodiment, there are included a plurality of secondparameters of one kind in the above Expressions (3)′ and (4) that arerespectively represented as π_(i)(1), π_(i)(2), . . . , π_(i)(N).Similarly, there are also included a plurality of second parameters oftwo kinds that are respectively represented as τ_(i)(1), τ_(i)(2), . . ., τ_(i)(N).

First, the operation executing part 41 accesses the storage part 5 (StepS1) and confirms whether or not the element calculation part 4 forcalculating another element included in j-th column or i-th row hasalready calculated the parameters a_(j)(m), π_(i)(m), b_(j)(m) andτ_(i)(m) the values of which are stored in the storage part 5 (Steps S21to S24).

Regarding the parameters which the element calculation part 4 forcalculating another element has already calculated in Steps S21 to S24,the operation executing part 41 acquires the values of the parametersfrom the storage part 5.

Regarding the parameters which the element calculation part 4 forcalculating another element has not yet calculated in Steps S21 to S24,the operation executing part 41 transmits the calculation signal forcalculating the parameter to the parameter calculation part 42.

Upon receipt of the calculation signal, the parameter calculation part42 calculates the value of the parameter corresponding to thecalculation signal and transmits the value to the operation executingpart 41 as well as to the storage part 5 (Steps S31 to S34).

The operation executing part 41 calculates f(m) using the value of eachparameter acquired from the storage part 5 and the parameter calculationpart 42 and stores the value in a predetermined area of the memory (StepS4).

Subsequently, the operation executing part 41 acquires the values off(1) to f(m) and sums these values (Step S5) and determines whether ornot the total sum converges to a value (Step S6).

It is noted that the determination of whether or not the total sumconverges is performed depending on, for example, whether or not a ratioof the total sum from f(1) to f(m−1) and that from f(1) to f(m) becomesa value or smaller.

In the case where it is determined in Step S6 that the total sum has notyet converged, the process is returned to Step S1 again while puttingn=m+1 (Step S7), and the process from Steps S1 to S5 is repeated untilit is determined in Step S6 that the total sum converges.

In the case where it is determined in Step S6 that the total sum hasconverged, the operation executing part 41 takes the convergence valueas the value of the element k_(ij) to be outputted to the particle sizedistribution calculation part (Step S8).

According the particle size distribution measuring apparatus 1 accordingto the present embodiment configured as described above, the followingeffects can be obtained.

Since the plurality of element calculation parts 4 compute in paralleland calculate all of the elements included in a certain column and acertain element calculation part 4 transmits the value of the parametercalculated in the computation process to the storage part 5 whileanother element calculation part 4 acquires the value of this parameterfrom the storage part 5 to thereby calculate the element, thecalculation time of the coefficient matrix K can be remarkably reducedas compared to the conventional case of calculating the elements one byone.

This effect is described in detail below.

In the case where the plurality of element calculation parts 4 computein parallel, for example, the elements of the first column, the twokinds of the first parameters a₁(n) and b₁(n) are used in common forcalculating each of the elements as shown in FIG. 6. Therefore, if anyone of the plurality of element calculation parts 4 calculates the firstparameter a₁(n) or b₁(n), another element calculation part 4 can acquirethis value from the storage part 5 to be used for calculating theelement.

Subsequently, in the case where the plurality of element calculationparts 4 compute in parallel, for example, the elements of the secondcolumn, the two kinds of the second parameters π_(i)(n) and τ_(i)(n)have been already calculated in a process of calculating the elementsincluded in the first column. Therefore, each of the element calculationparts 4 acquires the values of the two kinds of the second parametersπ_(i)(n) and τ_(i)(n) which have been already calculated from thestorage part 5 and the acquired values can be used for calculating eachof the elements. Similarly, this is also applied to the case ofcalculating the elements from the third column to the y-th column.

Therefore, as described above, according to the particle sizedistribution measuring apparatus 1 according to the present embodiment,the time required for calculating each of the elements can be reducedand the calculation time of the coefficient matrix K can be remarkablyreduced and the calculation time of the particle size distribution canbe reduced compared to the conventional case.

Note that the present invention should not be intended to be limited tothe above embodiment.

For example, although it is configured to compute in parallel theplurality of elements included in one column in the present embodiment,it may be also configured to compute in parallel the plurality ofelements included in one row as shown in an upper part of FIG. 7.

Further, as shown in a lower part of FIG. 7, it may be also configuredto compute in parallel the plurality of elements positioned diagonally.Also, in this case, the values of the parameters calculated by computingin parallel the plurality of elements can be used for calculatinganother element.

Moreover, a computing order of the respective columns can be freelyselected and it may be configured to sequentially calculate from they-th column to the first column. With this configuration, it is possibleto calculate in preference the elements which correspond to rearward orsideward diffracted/scattered lights and requiring a relatively longtime for converging in Step S6.

Further, in the above embodiment, although the parameter calculationpart 42 is configured so as to sequentially calculate the parameters a,π, b and τ, it may be configured so as to compute in parallel at leasttwo kinds of parameters among these parameters to be calculated.Further, it may be configured so as to compute in parallel the same kindof parameters like, for example, one kind of the first parametera_(j)(1) and one kind of the first parameter a_(j)(2).

With this configuration, the calculation time of the coefficient matrixK can be further reduced.

Furthermore, in the above embodiment, although the parameter calculationpart 42 transmits all of the calculated values of the parameters to thestorage part 5, it may be configured to transmit the values calculatedup to a predetermined number of terms (for example, n=100) to thestorage part 5 and not to transmit the values thereafter (for example,after n=101) to the storage part 5.

In the above embodiment, although the particle size distributioncalculation part 32 is intended to calculate the particle sizedistribution based on Expression (1), it may be intended to calculatethe particle size distribution based on an expression obtained by addinga term representing such as, for example, a noise to this Expression(1).

Further, although the vector s in Expression (1) is a vectorrepresenting a light intensity pattern of the diffracted/scattered lightobtained from the value of the light intensity signal outputted fromeach of the photodetectors 24, the vector s may be a vector using thevalue of the light intensity signal per se as the element.

In this case, in order to convert a vector q representing the particlesize distribution to the vector s, each of the elements of thecoefficient matrix K may be a value that is obtained by furtherconverting the value obtained from Expression (2) using such as, forexample, a distance from each of the photodetectors 24 to the cell 21.

Referring to the apparatus main body 2, although a laser device is usedas the light source 23 in the above embodiment, there may be used, forexample, an LED element that emits non-deflection light as the lightsource 23.

In this case, it is only necessary that the element calculation part 4is configured so as to calculate each of the elements based on a meanvalue of k₁ and k₂ obtained from the following two Expressions (5) and(6) that represent a vertical deflection component and a horizontaldeflection component of the light intensity.

$\begin{matrix}\left\lbrack {{Equation}\mspace{14mu} 6} \right\rbrack & \; \\{{k_{1}\left( {m,\alpha,\theta} \right)} = {\sum\limits_{n = 1}^{N}\; {\frac{{2\; n} + 1}{n\left( {n + 1} \right)}\begin{bmatrix}{{{a\left( {n,m,\alpha} \right)} \times {\pi \left( {n,{\cos \; \theta}} \right)}} +} \\{{b\left( {n,m,\alpha} \right)} \times {\tau \left( {n,{\cos \; \theta}} \right)}}\end{bmatrix}}}} & (5) \\{{k_{2}\left( {m,\alpha,\theta} \right)} = {\sum\limits_{n = 1}^{N}\; {\frac{{2\; n} + 1}{n\left( {n + 1} \right)}\begin{bmatrix}{{{a\left( {n,m,\alpha} \right)} \times {\pi \left( {n,{\cos \; \theta}} \right)}} +} \\{{b\left( {n,m,\alpha} \right)} \times {\tau \left( {n,{\cos \; \theta}} \right)}}\end{bmatrix}}}} & (6)\end{matrix}$

Note that this Expression (5) is identical to Expression (2) and thisexpression can be used in common even if the light from the light source23 is deflection light or non-deflection light.

In addition, the present invention should not be limited to the aboveembodiment and each of the partial components can be combined, andvarious modifications are of course possible within the scope unlessdeparting from the intended spirit thereof.

REFERENCE SIGNS LIST

-   1 . . . Particle size distribution measuring apparatus-   2 . . . Apparatus body-   3 . . . Operation part-   31 . . . Coefficient matrix calculation part-   4 . . . Element calculation part-   41 . . . Operation executing part-   42 . . . Parameter calculation part-   5 . . . Storage part

1. A particle size distribution measuring apparatus comprising: a lightsource for irradiating light to particles to be measured; a plurality ofphotodetectors for detecting light intensities of diffracted/scatteredlights caused by the irradiation of the light; and an operation part forreceiving light intensity signals outputted from the respectivephotodetectors and calculating a particle size distribution of theparticles based on the fact that a vector s is represented by apredetermined expression including a product of a vector q and acoefficient matrix K, wherein the operation part is adapted to calculatevalues of a plurality of first parameters that depend on the particlesizes of the particles and a plurality of second parameters that dependon spread angles of the diffracted/scattered lights, the first andsecond parameters being used for calculating one element among elementsof the coefficient matrix K, and store at least one of the values to beused for calculating another element of the coefficient matrix K, here,the vector s is a vector representing a light intensity pattern at everyangle of the diffracted/scattered lights obtained from values of thelight intensity signals outputted from the respective photodetectors,the vector q is a vector representing the particle size distribution ofthe particles to be measured, and the coefficient matrix K is a matrixfor converting the vector q to the vector s.
 2. The particle sizedistribution measuring apparatus according to claim 1, wherein theoperation part calculates an element of a position where a certain rowand a certain column intersect using the values of the first parametersstored at a time of calculating the elements included in the row and thevalues of the second parameters stored at a time of calculating theelements included in the column among the elements of the coefficientmatrix K, based on a following expression:${k\left( {m,\alpha,\theta} \right)} = {\sum\limits_{n = 1}^{N}\; {\frac{{2\; n} + 1}{n\left( {n + 1} \right)}\begin{bmatrix}{{{a\left( {n,m,\alpha} \right)} \times {\pi \left( {n,{\cos \; \theta}} \right)}} +} \\{{b\left( {n,m,\alpha} \right)} \times {\tau \left( {n,{\cos \; \theta}} \right)}}\end{bmatrix}}}$ here, k is a value of each of the elements of thecoefficient matrix K, m is a refractive index of each of the particlesto be measured, α is a value associated with each of the particle sizesof the particles to be measured, θ is a spread angle ofdiffracted/scattered light, a and b are the first parameters that dependon the refractive index of the particle and particle size, π and τ arethe second parameters that depend on the diffracted/scattered lights,and N is a value that represents the last term when the operating partoperates a sum represented by a sigma symbol.
 3. A recording mediumrecorded with a program to be loaded on a particle size distributionmeasuring apparatus that comprises: a light source for irradiating lightto particles to be measured; a plurality of photodetectors for detectinglight intensities of diffracted/scattered lights caused by theirradiation of the light; and an operation part for receiving lightintensity signals outputted from the respective photodetectors andcalculating a particle size distribution of the particles based on thefact that a vector s is represented by a predetermined expressionincluding a product of a vector q and a coefficient matrix K, whereinthe program renders the operation part to exhibit a function of:calculating values of a plurality of first parameters that depend on theparticle sizes of the particles and a plurality of second parametersthat depend on spread angles of the diffracted/scattered lights, thefirst and second parameters being used for calculating one element amongelements of the coefficient matrix K; storing at least one of thevalues; and calculating another element of the coefficient matrix K,here, the vector s is a vector representing a light intensity pattern atevery angle of the diffracted/scattered lights obtained from values ofthe light intensity signals outputted from the respectivephotodetectors, the vector q is a vector representing the particle sizedistribution of the particles to be measured, and the coefficient matrixK is a matrix for converting the vector q to the vector s.